\((\frac{1}{2}-1)\times(\frac{1}{3}-1)...\times(\frac{1}{2009}-1)\)
C=\((1+\frac{2}{3})\times(1+\frac{2}{5})\times(1+\frac{2}{7})\times...\times(1+(\frac{2}{2009})\times(1+\frac{2}{2011})\)
\(C=\left(1+\frac{2}{3}\right)\cdot\left(1+\frac{2}{5}\right)\cdot\left(1+\frac{2}{7}\right)\cdot\cdot\cdot\cdot\cdot\left(1+\frac{2}{2009}\right)\cdot\left(1+\frac{2}{2011}\right)\)
\(C=\frac{5}{3}\cdot\frac{7}{5}\cdot\frac{9}{7}\cdot\cdot\cdot\cdot\cdot\frac{2011}{2009}\cdot\frac{2013}{2011}\)
\(C=\frac{5\cdot7\cdot9\cdot\cdot\cdot\cdot\cdot2011\cdot2013}{3\cdot5\cdot7\cdot\cdot\cdot\cdot\cdot2009\cdot2011}\)
\(C=\frac{2013}{3}\)
đề bài của bài là tính
ai nhanh mk k cho
\(C=\left(1+\frac{2}{3}\right).\left(1+\frac{2}{5}\right).....\left(1+\frac{2}{2009}\right).\left(1+\frac{2}{2011}\right)\)
\(C=1\left(\frac{2}{3}+\frac{2}{5}+...+\frac{2}{2009}+\frac{2}{2011}\right)\)
\(\frac{1}{2}C=\frac{1}{3}+\frac{1}{5}+...+\frac{1}{2009}+\frac{1}{2011}\)
\(\frac{1}{2}C=\frac{1}{3+5+...+2011}\)
\(\frac{1}{2}C=\frac{1}{1012035}\)
\(\Rightarrow C=\frac{1}{1012035}:\frac{1}{2}=\frac{2}{1012035}\)
Tính P = \(\left(1+\frac{1}{3}\right)\times\left(1+\frac{1}{2\times4}\right)\times\left(1+\frac{1}{3\times5}\right)\times\left(1+\frac{1}{4\times6}\right)\times...\times\left(1+\frac{1}{2009\times2011}\right)\)
(1+\(\frac{1}{3}\)) x (1+\(\frac{1}{2x4}\)) x(1+\(\frac{1}{3x5}\))x(1+\(\frac{1}{4x6}\)) x .....x (1+ \(\frac{1}{2009x2011}\))
= \(\frac{2}{1x3}\)x \(\frac{2}{2x4}\)x \(\frac{2}{3x5}\)x \(\frac{2}{4x6}\)x....x \(\frac{2}{2009x2011}\)
= ..................
đến đây tự làm nhé
Kết quả của phép tính:
\(\left(-2\right)\times\left(-1\frac{1}{2}\right)\times\left(-1\frac{1}{3}\right)..........\times\left(-1\frac{1}{2009}\right)\times\left(-1\frac{1}{2010}\right)\)
\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+......+\frac{1}{y\times\left(y+1\right):2}=\frac{2009}{2011}\)
Tìm \(x\):
\(\left(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+.....\frac{1}{2009\times2010}\right)\times x=2009\)
\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+....+\frac{1}{2009\cdot2010}\right)\cdot x=2009\)
\(\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2009}-\frac{1}{2010}\right)\cdot x=2009\)
\(\left(1-\frac{1}{2010}\right)\cdot x=2009\)
\(\frac{2009}{2010}\cdot x=2009\)
\(x=2009:\frac{2009}{2010}\)
\(x=2010\)
\(\left(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}+....+\frac{1}{2009}-\frac{1}{2010}\right).x=2009\)
\(\left(\frac{1}{1}-\frac{1}{2010}\right).x=2009\)
\(\frac{2009}{2010}.x=2009\)
\(x=2009:\frac{2009}{2010}\)
\(x=2010\)
Tìm tích:
1.\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\left(\frac{1}{4}+1\right)\times...\times\left(\frac{1}{999}+1\right)\)
2.\(\left(\frac{1}{2}-1\right)\times\left(\frac{1}{3}-1\right)\times\left(\frac{1}{4}-1\right)\times...\times\left(\frac{1}{1000}-1\right)\)
3.\(\frac{3}{2^2}\times\frac{8}{3^2}\times\frac{15}{4^2}\times...\times\frac{99}{10^2}\)
biết làm bài 1 thôi
\(\left(\frac{1}{2}+1\right)\times\left(\frac{1}{3}+1\right)\times\cdot\cdot\cdot\times\left(\frac{1}{999}+1\right)\)
= \(\frac{3}{2}\times\frac{4}{3}\times\frac{5}{4}\times\cdot\cdot\cdot\times\frac{1000}{999}\)
lượt bỏ đi còn :
\(\frac{1000}{2}=500\)
Tính nhanh:\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)
\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+...+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{6}\)
\(=\frac{3+6-2}{12}=\frac{7}{12}\)
\(\frac{1}{2}\)* \(\frac{1}{2}\)+ \(\frac{1}{2}\)*\(\frac{1}{3}\)+ \(\frac{1}{3}\)* \(\frac{1}{4}\)+ \(\frac{1}{4}\)* \(\frac{1}{5}\)+ \(\frac{1}{5}\)* \(\frac{1}{6}\)
=\(\frac{1}{2}\)* \(\frac{1}{6}\)= \(\frac{1}{12}\)
( Những phân số khác nhau bạn loại đi nhé tại mình ko làm được bước đó trên này bạn thông cảm nhé ! )
\(\frac{1}{2}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+...+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{4}+\frac{1}{2}-\frac{1}{6}\)
\(=\frac{7}{12}\)
\(\frac{1}{1}\times\frac{1}{2}+\frac{1}{2}\times\frac{1}{3}+\frac{1}{3}\times\frac{1}{4}+\frac{1}{4}\times\frac{1}{5}+\frac{1}{5}\times\frac{1}{6}\)
\(=\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(=\frac{30}{60}+\frac{10}{60}+\frac{5}{60}+\frac{3}{60}+\frac{2}{60}=\frac{50}{60}=\frac{5}{6}\)
=\(\frac{1}{2}\)+\(\frac{1}{6}\)+\(\frac{1}{12}\)+\(\frac{1}{20}\)+\(\frac{1}{30}\)=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+\(\frac{1}{3}\)-\(\frac{1}{4}\)+\(\frac{1}{4}\)-\(\frac{1}{5}\)+\(\frac{1}{5}\)-\(\frac{1}{6}\)
=1-\(\frac{1}{6}\)
=\(\frac{5}{6}\)
C1:\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}\)
\(\Rightarrow\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{6}\)
\(\Rightarrow\frac{5}{6}\)
C2:\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(\Rightarrow\frac{1}{1}-\frac{1}{6}\)
\(\Rightarrow\frac{5}{6}\)
B = \(\frac{(\frac{1}{5}-\frac{2}{7})\times\frac{3}{4}-\frac{3}{4}\times(\frac{1}{3}-\frac{2}{7})}{\frac{1}{5}\times\frac{2}{7}-\frac{1}{3}\times(\frac{2}{7}+\frac{3}{9})+\frac{3}{9}\times\frac{1}{5}}\)
ồ cuk dễ nhỉ
Nếu các bn thích thì ...........
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